POINTWISE: Predicting Points and Valuing Decisions in Real Time with NBA Optical Tracking Data Dan Cervone†, Alexander D’Amour†, Luke Bornn†, and Kirk Goldsberry‡ Department of Statistics† and Institute for Quantitative Social Science‡ Harvard University Cambridge, MA, USA, 02138 Email: [email protected] Abstract Basketball is a game of decisions; at any moment, a player can change the character of a possession by choosing to pass, dribble, or shoot. The current state of basketball analytics, however, provides no way to quantitatively evaluate the vast majority of decisions that players make, as most metrics are driven by events that occur at or near the end of a possession, such as points, turnovers, and assists. We propose a framework for using player-tracking data to assign a point value to each moment of a possession by computing how many points the offense is expected to score by the end of the possession, a quantity we call expected possession value (EPV). EPV allows analysts to evaluate every decision made during a basketball game – whether it is to pass, dribble, or shoot – opening the door for a multitude of new metrics and analyses of basketball that quantify value in terms of points. In this paper, we propose a modeling framework for estimating EPV, present results of EPV computations performed using player- tracking data from the 2012-13 season, and provide several examples of EPV-derived metrics that answer real basketball questions. A new microeconomics for the NBA Basketball players, coaches, and fans often compare a possession to a high-speed chess match, where teams employ tactics that do not necessarily generate points immediately, but can yield higher-value opportunities several “moves” down the line. Watching the game in this way can reveal that the decisive moment in a given possession may not have been the open shot at the end, but the pass that led to the open shot, or even the preceding drive that collapsed the defense. These ideas lie at the heart of offensive strategies and the decisions that players make over the course of a possession. Unfortunately, contemporary basketball analytics fail to account for this core idea. Despite many recent innovations, most advanced metrics (PER [1] and +/- variations [2], for example) remain based on simple tallies relating to the terminal states of possessions like points, rebounds, and turnovers. While these have shed light on the game, they are akin to analyzing a chess match based only on the move that resulted in checkmate, leaving unexplored the possibility that the key move occurred several turns before. This leaves a major gap to be filled, as an understanding of how players contribute to the whole possession – not just the events that end it – can be critical in evaluating players, assessing the quality of their decision-making, and predicting the success of particular in-game tactics. The major obstacle to closing this gap is the current inability to evaluate the individual tactical decisions that form the substructure of every possession of every basketball game. For example, there is no current method to estimate the value of a dribble penetration or to compare the option of taking a contested shot to the option of passing to an open teammate. In this paper, we propose and implement a framework that removes this obstacle. Using player-tracking data, we develop a coherent, quantitative representation of a whole possession that summarizes each moment of the possession in terms of the number of points the offense is expected to score – a quantity we call expected possession value, or EPV (see Figure 1 for an illustration of EPV). We accomplish this by specifying and fitting a probabilistic model that encodes how ball handlers make decisions based on the spatial configuration of the players on the court. 2014 Research Paper Competition Presented by: Figure 1. Diagram of EPV as a weighted average of the values of the ballcarrier's (Leonard's) decisions and the probability of making each decision. We also consider the possibility of Leonard dribbling to a different area or driving toward the basket, as well as turning the ball over, but these are omitted from the above diagram for conceptual clarity. EPV assigns a point value to every tactical option available to a player at each moment of a possession, allowing analysts to evaluate each decision that a player makes. For example, passing to a wide open shooter in the corner or near the basket is worth more expected points than to a covered player in a similar place. EPV thus opens up new avenues of basketball analysis that focus on decision-making, opportunity creation and prevention, and optimal responses that were not possible before. Just as the notion of utility made quantitative analysis of everyday decisions possible in microeconomics, we believe EPV lays the foundation for quantitative decision analysis in the NBA. This paper has four parts1. In Part 1, we give a brief overview of the possession model we use to compute EPV. Part 2 showcases the raw results of our EPV computations using our current specification of the possession model, showing how EPV changes in real time as a possession unfolds. Part 3 introduces several examples of how EPV can be used to answer real basketball questions. These examples are in no way an exhaustive list, but should be instructive of how wide-reaching EPV can be as a framework for basketball analytics. Finally, in Part 4, we discuss how EPV-based analysis can be extended in future work. 1 Computing EPV with a possession model: What happens next? EPV is a conditional expectation – the expected number of points the offense will score, given the spatial configuration of the players and ball at time during the possession ): [ ] By definition, the current EPV of a possession is the weighted average of the outcomes of all future paths that the possession could take. Calculating this requires a model that defines a probability distribution over what the ballhandler is likely to do next, given the spatial configuration of the players on the court, as we need to understand what future paths the possession can take and how likely they are given the present state. We call this model the 1 Because optical tracking data has been presented several times at the Sloan conference, we have placed a description of the data in the appendix. 2014 Research Paper Competition 2 Presented by: possession model. Using a Markovian assumption2, the possession model allows us to estimate both (a) the probability that a player will make a particular decision in a given situation and (b) the resulting EPV of the possession after the player makes that decision. Taken together, we learn both how valuable any moment in a possession is, as well as the features of the offense's configuration that produce this value. For an illustration of this breakdown of EPV, see Figure 1. Our possession model breaks down a player's options into discrete actions that may take several seconds to complete (e.g., passing or shooting) or continuous actions that evolve instantaneously (e.g., moving to the left or right). We call the former actions macrotransitions and the latter actions microtransitions. Using this breakdown, we can rewrite EPV at time during a possession by conditioning on the ballhandler's next action during a small time window ( ): ) [ ] [ ] ] ] ) ) [ ] ] ] ) In our current implementation, we define passes, shots, and turnovers as macrotransitions, and all movements that players make with the ball as microtransitions. However, if one were able to identify additional spatiotemporal motifs, either by algorithmic sophistication or the input of coaches or players, it would be possible to incorporate other actions such as drives to the hoop as additional macrotransitions. The macro/microtransition dichotomy facilitates calculating components of (1) using statistical models. The macrotransition probabilities ] ) (e.g., the instantaneous probability that a player will pass or shoot the ball) respond to the full-resolution spatial configuration of the players, and are therefore the most nuanced components. We compute these using competing risks, a statistical framework for modeling the occurrence of discrete events in continuous time [3, 4], incorporating situational covariates (e.g., presence of defender between player and teammate), and spatially-smoothed random effects that capture individual players' tendencies [5]. We compute [ ] ] by modeling a coarsened version of the court space as a homogeneous Markov chain (a common technique in baseball [6] and football [7]). We compute the final components in (1), based on microtransitions, from the macrotransition components and some basic mathematical assumptions of local space-time smoothness. The exact specification and technical details for fitting our possession model for each player in the NBA are beyond the scope of the paper, and are the subject of a forthcoming statistical article. Indeed, one major challenge of using data sets as large and rich as optical tracking data is implementing statistical models that are flexible enough to incorporate subtle spatial patterns in players' tendencies while being robust enough to avoid overfitting the occasional abnormal behavior we observe – the Dwight Howard corner 3, for instance. Standard techniques such as regression, analysis of variance, and generalized linear models are ill-suited to these problems. The competing risk models we use to estimate decision probabilities in different situations respond to small but meaningful changes in the data space, such as the ball carrier's exact location on the court and the positions of the defenders relative to his passing options. However, the sophistication of such models carries a heavy computational cost – using cutting-edge algorithms [8, 9], our possession model still requires several hours to fit using hundreds of processors and over 4 terabytes of memory.